# American Institute of Mathematical Sciences

March  2021, 29(1): 1681-1689. doi: 10.3934/era.2020086

## Some properties for almost cellular algebras

 1 School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China 2 Department of Mathematics, Shanghai University, Shanghai 200444, China

* Corresponding author: Nan Gao

Received  April 2020 Revised  June 2020 Published  March 2021 Early access  August 2020

Fund Project: The first author is supported by National Natural Science Foundation of China Project (No. 11901146), and the second author is supported by National Natural Science Foundation of China Project (No.11771272)

In this paper, we will investigate some properties for almost cellular algebras. We compare the almost cellular algebras with quasi-hereditary algebras, which are known to carry any homological and categorical structures. We prove that any almost cellular algebra is the iterated inflation and obtain some sufficient and necessary conditions for an almost cellular algebra $\mathrm{A}$ to be quasi-hereditary.

Citation: Yongjie Wang, Nan Gao. Some properties for almost cellular algebras. Electronic Research Archive, 2021, 29 (1) : 1681-1689. doi: 10.3934/era.2020086
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